Annual Review of Fluid Mechanics - Volume 55, 2023

In the past few decades various particle image–based volumetric flow measurement techniques have been developed that have demonstrated their potential in accessing unsteady flow properties quantitatively in various experimental applications in fluid mechanics. In this review, we focus on physical properties and circumstances of 3D particle–based measurements and what knowledge can be used for advancing reconstruction accuracy and spatial and temporal resolution, as well as completeness. The natural candidate for our focus is 3D Lagrangian particle tracking (LPT), which allows for position, velocity, and acceleration to be determined alongside a large number of individual particle tracks in the investigated volume. The advent of the dense 3D LPT technique Shake-The-Box in the past decade has opened further possibilities for characterizing unsteady flows by delivering input data for powerful data assimilation techniques that use Navier–Stokes constraints. As a result, high-resolution Lagrangian and Eulerian data can be obtained, including long particle trajectories embedded in time-resolved 3D velocity and pressure fields.

Since its birth in the 1920s, quantum mechanics has motivated and advanced the analysis of linear operators. In this effort, it significantly contributed to the development of sophisticated mathematical tools in spectral theory. Many of these tools have also found their way into classical fluid mechanics and enabled elegant and effective solution strategies as well as physical insights into complex fluid behaviors. This review provides supportive evidence for synergistically adopting mathematical techniques beyond the classical repertoire, both for fluid research and for the training of future fluid dynamicists. Deeper understanding, compelling solution methods, and alternative interpretations of practical problems can be gained by an awareness of mathematical techniques and approaches from quantum mechanics. Techniques such as spectral analysis, series expansions, considerations on symmetries, and integral transforms are discussed, and applications from acoustics and incompressible flows are presented with a quantum mechanical perspective.

Since the seminal studies by Osborne Reynolds in the nineteenth century, pipe flow has served as a primary prototype for investigating the transition to turbulence in wall-bounded flows. Despite the apparent simplicity of this flow, various facets of this problem have occupied researchers for more than a century. Here we review insights from three distinct perspectives: (a) stability and susceptibility of laminar flow, (b) phase transition and spatiotemporal dynamics, and (c) dynamical systems analysis of the Navier—Stokes equations. We show how these perspectives have led to a profound understanding of the onset of turbulence in pipe flow. Outstanding open points, applications to flows of complex fluids, and similarities with other wall-bounded flows are discussed.

Rotation with thermally induced buoyancy governs many astrophysical and geophysical processes in the atmosphere, ocean, sun, and Earth's liquid-metal outer core. Rotating Rayleigh–Bénard convection (RRBC) is an experimental system that has features of rotation and buoyancy, where a container of height H and temperature difference Δ between its bottom and top is rotated about its vertical axis with angular velocity Ω. The strength of buoyancy is reflected in the Rayleigh number (∼H³Δ) and that of the Coriolis force in the Ekman and Rossby numbers (∼Ω⁻¹). Rotation suppresses the convective onset, introduces instabilities, changes the velocity boundary layers, modifies the shape of thermal structures from plumes to vortical columns, affects the large-scale circulation, and can decrease or enhance global heat transport depending on buoyant and Coriolis forcing. RRBC is an extremely rich system, with features directly comparable to geophysical and astrophysical phenomena. Here we review RRBC studies, suggest a unifying heat transport scaling approach for the transition between rotation-dominated and buoyancy-dominated regimes in RRBC, and discuss non-Oberbeck–Boussinesq and centrifugal effects.

A rotating detonation engine (RDE) is a realization of pressure-gain combustion, wherein a traveling detonation wave confined in a chamber provides shock-based compression along with chemical heat release. Due to the high wave speeds, such devices can process high mass flow rates in small volumes, leading to compact and unconventional designs. RDEs involve unsteady and multiscale physics, and their operational characteristics are determined by an equilibrium between large- and small-scale processes. While RDEs can provide a significant theoretical gain in efficiency, achieving this improvement requires an understanding of the multiscale coupling. Specifically, unavoidable nonidealities, such as unsteady mixing, secondary combustion, and multiple competing waves associated with practical designs, need to be understood and managed. The secondary combustion processes arise from fuel/air injection and unsteady and incomplete mixing, and can create spurious losses. In addition, a combination of multiple detonation and secondary waves compete and define the dynamical behavior of mixing, heat release distribution, and the overall mode of operation of the device. This review discusses the current understanding of such nonidealities and describes the tools and techniques used to gain insight into the extreme unsteady environment in such combustors.

The dissolution of minute concentration of polymers in wall-bounded flows is well-known for its unparalleled ability to reduce turbulent friction drag. Another phenomenon, elasto-inertial turbulence (EIT), has been far less studied even though elastic instabilities have already been observed in dilute polymer solutions before the discovery of polymer drag reduction. EIT is a chaotic state driven by polymer dynamics that is observed across many orders of magnitude in Reynolds number. It involves energy transfer from small elastic scales to large flow scales. The investigation of the mechanisms of EIT offers the possibility to better understand other complex phenomena such as elastic turbulence and maximum drag reduction. In this review, we survey recent research efforts that are advancing the understanding of the dynamics of EIT. We highlight the fundamental differences between EIT and Newtonian/inertial turbulence from the perspective of experiments, numerical simulations, instabilities, and coherent structures. Finally, we discuss the possible links between EIT and elastic turbulence and polymer drag reduction, as well as the remaining challenges in unraveling the self-sustaining mechanism of EIT.

A common feature of many free surface flows—drop/bubble breakup or coalescence and film/sheet rupture—is the occurrence of hydrodynamic singularities. Accurately computing such flows with continuum mechanical, multidimensional free surface flow algorithms is a challenging task given these problems’ multiscale nature, which necessitates capturing dynamics occurring over disparate length scales across 5–6 orders of magnitude. In drop breakup, the thinning of fluid threads that form and eventually pinch-off must be simulated until the thread's radius is about 10 nm. When two drops approach one another, the thickness of the fluid film separating them must fall below 10 nm before coalescence is said to have occurred. If the initial drop radii are 1 mm, simulations must remain faithful to the physics as thread radius or film thickness falls from 10⁻³ m to below 10⁻⁸ m. Here we review significant findings in interfacial flows with hydrodynamic singularities spearheaded by sharp interface algorithms. These multidimensional algorithms can achieve resolution that to date has only been possible with the use of simple 1D evolution equations.